MenuColloquium - Eviatar Procaccia
Date: February 3, 2015
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Eviatar Proaccia, University of California, LA
Description:
Title:Geometric homogeneity in disordered spatial processes.
Abstract:
Experimentalists observed that microscopically disordered systems exhibit homogeneous geometry on a macroscopic scale. In the last decades elegant tools were created to mathematically assert such phenomenon. The classical geometric results, such as asymptotic graph distance and isoperimetry of large sets, are restricted to i.i.d. Bernoulli percolation. There are many interesting models in statistical physics and probability theory, that exhibit long range correlation. In this talk I will survey the theory, and discuss a new result proving, for a general class of correlated percolation models, that a random walk on almost every configuration, scales diffusively to Brownian motion with non-degenerate diffusion matrix. As a corollary we obtain new results for the Gaussian free field, Random Interlacements and the vacant set of Random Interlacements. In the heart of the proof is a new isoperimetry result for correlated models.
